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Abstract Several new methods are proposed that can diagnose the interscale transfer (or spectral flux) of kinetic energy (KE) and other properties in oceanic and broader geophysical systems, using integrals of advective structure functions and Bessel functions (herein “Bessel methods”). The utility of the Bessel methods is evaluated using simulations of anisotropic flow within two-dimensional (2D), surface quasigeostrophic (SQG), and two-layer QG systems. The Bessel methods diagnose various spectral fluxes within all of these systems, even under strong anisotropy and complex dynamics (e.g., multiple cascaded variables, coincident and opposing spectral fluxes, and nonstationary systems). In 2D turbulence, the Bessel methods capture the inverse KE cascade at large scales and the downscale enstrophy cascade (and associated downscale energy flux) at small scales. In SQG turbulence, the Bessel methods capture the downscale buoyancy variance cascade and the coincident upscale wavenumber-dependent KE flux. In QG turbulence, the Bessel methods capture the upscale kinetic energy flux. It is shown that these Bessel methods can be applied to data with limited extent or resolution, provided the scales of interest are captured by the range of separation distances. The Bessel methods are shown to have several advantages over other flux-estimation methods, including the ability to diagnose downscale energy cascades and to identify sharp transition scales. Analogous Bessel methods are also discussed for third-order structure functions, along with some caveats due to boundary terms. Significance StatementBig ocean eddies play an important role in Earth’s energy cycle by moving energy to both larger and smaller scales, but it is difficult to measure these “eddy energy fluxes” from oceanic observations. We develop a new method to estimate eddy energy fluxes that utilizes spatial differences between pairs of points and can be applied to various ocean data. This new method accurately diagnoses key eddy energy flux properties, as we demonstrate using idealized numerical simulations of various large-scale ocean systems.
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Two-dimensional isotropic inertia–gravity wave turbulence
We present an idealized study of rotating stratified wave turbulence in a two-dimensional vertical slice model of the Boussinesq equations, focusing on the peculiar case of equal Coriolis and buoyancy frequencies. In this case the fully nonlinear fluid dynamics can be shown to be isotropic in the vertical plane, which allows the classical methods of isotropic turbulence to be applied. Contrary to ordinary two-dimensional turbulence, here a robust downscale flux of total energy is observed in numerical simulations that span the full parameter regime between Ozmidov and forcing scales. Notably, this robust downscale flux of the total energy does not hold separately for its various kinetic and potential components, which can exhibit both upscale and downscale fluxes, depending on the parameter regime. Using a suitable extension of the classical Kármán–Howarth–Monin equation, exact expressions that link third-order structure functions and the spectral energy flux are derived and tested against numerical results. These expressions make obvious that even though the total energy is robustly transferred downscale, the third-order structure functions are sign indefinite, which illustrates that the sign and the form of measured third-order structure functions are both crucially important in determining the direction of the spectral energy transfer.
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- Award ID(s):
- 1813891
- PAR ID:
- 10120396
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 872
- ISSN:
- 0022-1120
- Page Range / eLocation ID:
- 752 to 783
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2019.406
